Preheat the oven to 325°F. Season the short ribs with salt and pepper. In a large Dutch oven, heat the olive oil over medium-high heat. Sear the short ribs on all sides until browned, about 8-10 minutes. Remove and set aside.
In the same pot, add the onion, carrots, and celery. Sauté until softened, about 5 minutes. Add the garlic and cook for an additional minute.
Pour in the red wine, scraping up any browned bits from the bottom of the pot. Allow it to simmer for 2-3 minutes.
Stir in the crushed tomatoes, beef broth, oregano, thyme, and return the short ribs to the pot. Bring to a simmer, cover, and transfer to the oven. Cook for 2.5 to 3 hours, until the meat is tender and falling off the bone.
While the ragu is cooking, prepare the mashed potatoes. Boil the potatoes in salted water until tender, about 15-20 minutes. Drain and return to the pot.
Add the butter, milk, and Parmesan cheese to the potatoes. Mash until smooth and creamy. Season with salt and pepper to taste.
Once the short ribs are done, remove them from the pot and shred the meat, discarding the bones. Return the shredded meat to the sauce and stir to combine.
Cook the pasta according to package instructions. Drain and toss with the ragu. Serve the pasta topped with Parmesan mashed potatoes.